We apply the method of projecting functions onto convex cones in Hilbert spaces to derive sharp upper bounds for the expectations of spacings from i.i.d. samples coming from restricted families of distributions. Two families are considered: distributions with decreasing density and with decreasing failure rate. We also characterize the distributions for which the bounds are attained.
We consider the simulation of transient performance measures of high reliable fault-tolerant computer systems. The most widely used mathematical tools to model the behavior of these systems are Markov processes. Here, we deal basically with the simulation of the mean time to failure (MTTF) and the reliability, R(t), of the system at time t. Some variance reduction techniques are used to reduce the simulation time. We will combine two of these techniques: Importance Sampling and Conditioning...
Marshall and Olkin (1997) introduced a new family of distributions by adding a tilt parameter. The same family was obtained by Kirmani and Gupta (2001) as the proportional odds model, which had been proposed by Clayton (1974). In this paper, stochastic ordering of distributions from this class and preservation of classes of life distributions by adding a parameter are obtained. The proportional odds family is also considered as a family of weighted distributions.
Doubly truncated data appear in some applications with survival and astrological data. Analogous to the doubly truncated discrimination measure defined by Misagh and Yari (2012), a generalized discrimination measure between two doubly truncated non-negative random variables is proposed. Several bounds are obtained. It is remarked that the proposed measure can never be equal to a nonzero constant which is independent of the left and right truncated points. The effect of monotone transformations on...
Let denote the failure rate function of the . and let denote the failure rate function of the mean residual life distribution. In this paper we characterize the distribution functions for which and we estimate when it is only known that or is bounded.
This article presents a new concept for a statistical fault detection system, including the detection, diagnosis, and prediction of faults. Theoretical material has been collected to provide a complete algorithm making possible the design of a usable system for statistical inference on the basis of the current value of a symptom vector. The use of elements of artificial intelligence enables self-correction and adaptation to changing conditions. The mathematical apparatus is founded on the methodology...
Recently the order preserving property of estimators has been intensively studied, e.g. by Gan and Balakrishnan and collaborators. In this paper we prove the stochastic monotonicity of moment estimators of gamma distribution parameters using the standard coupling method and majorization theory. We also give some properties of the moment estimator of the shape parameter and derive an approximate confidence interval for this parameter.
The stress-strength model is proposed based on the -generalized order statistics and the corresponding concomitant. For the dependency between -generalized order statistics and its concomitant, a bivariate copula expansion is considered and the stress-strength model is obtained for two special cases of order statistics and upper record values. In the particular case of copula function, the generalized Farlie-Gumbel-Morgenstern bivariate distribution function is considered with proportional reversed...
En este trabajo consideramos estimaciones no paramétricas de las funciones de razón de fallo y supervivencia en fiabilidad haciendo uso de suavizaciones no paramétricas de la función de distribución empírica (datos no censurados) y de la distribución de Kaplan-Meier (datos censurados). Se obtienen sesgos, varianzas y distribuciones asintóticas de los estimadores aquí propuestos probándose mediante técnicas de expansiones de segundo orden la eficiencia de éstos respecto de otras estimaciones introducidas...
A model of a heterogeneous population partitioned into a finite number of classes according an exchangeable equivalence relation is studied. With this motivation the properties of exchangeable equivalence relations are investigated and, in particular, the structure of its equivalence classes is characterized.